183 lines
4.5 KiB
C
183 lines
4.5 KiB
C
#include <math.h>
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#include <float.h>
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#include "common.h"
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#ifdef FUNCTION_PROFILE
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#include "functable.h"
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#endif
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#ifndef CBLAS
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void NAME(FLOAT *DA, FLOAT *DB, FLOAT *C, FLOAT *S){
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#else
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void CNAME(void *VDA, void *VDB, FLOAT *C, void *VS) {
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FLOAT *DA = (FLOAT*) VDA;
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FLOAT *DB = (FLOAT*) VDB;
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FLOAT *S = (FLOAT*) VS;
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#endif /* CBLAS */
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#ifdef DOUBLE
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long double safmin = DBL_MIN;
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long double rtmin = sqrt(DBL_MIN/DBL_EPSILON);
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#else
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long double safmin = FLT_MIN;
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long double rtmin = sqrt(FLT_MIN/FLT_EPSILON);
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#endif
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FLOAT da_r = *(DA+0);
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FLOAT da_i = *(DA+1);
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FLOAT db_r = *(DB+0);
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FLOAT db_i = *(DB+1);
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//long double r;
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FLOAT S1[2];
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FLOAT R[2];
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long double d;
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FLOAT ada = da_r * da_r + da_i * da_i;
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FLOAT adb = db_r * db_r + db_i * db_i;
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PRINT_DEBUG_NAME;
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IDEBUG_START;
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FUNCTION_PROFILE_START();
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if (db_r == ZERO && db_i == ZERO) {
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*C = ONE;
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*(S + 0) = ZERO;
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*(S + 1) = ZERO;
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return;
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}
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long double safmax = 1./safmin;
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#if defined DOUBLE
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long double rtmax = safmax /DBL_EPSILON;
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#else
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long double rtmax = safmax /FLT_EPSILON;
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#endif
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*(S1 + 0) = *(DB + 0);
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*(S1 + 1) = *(DB + 1) *-1;
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if (da_r == ZERO && da_i == ZERO) {
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*C = ZERO;
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if (db_r == ZERO) {
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(*DA) = fabsl(db_i);
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*S = *S1 /(*DA);
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*(S+1) = *(S1+1) /(*DA);
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return;
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} else if ( db_i == ZERO) {
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*DA = fabsl(db_r);
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*S = *S1 /(*DA);
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*(S+1) = *(S1+1) /(*DA);
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return;
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} else {
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long double g1 = MAX( fabsl(db_r), fabsl(db_i));
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rtmax =sqrt(safmax/2.);
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if (g1 > rtmin && g1 < rtmax) { // unscaled
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d = sqrt(adb);
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*S = *S1 /d;
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*(S+1) = *(S1+1) /d;
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*DA = d ;
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*(DA+1) = ZERO;
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return;
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} else { // scaled algorithm
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long double u = MIN ( safmax, MAX ( safmin, g1));
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FLOAT gs_r = db_r/u;
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FLOAT gs_i = db_i/u;
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d = sqrt ( gs_r*gs_r + gs_i*gs_i);
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*S = gs_r / d;
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*(S + 1) = (gs_i * -1) / d;
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*DA = d * u;
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*(DA+1) = ZERO;
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return;
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}
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}
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} else {
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FLOAT f1 = MAX ( fabsl(da_r), fabsl(da_i));
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FLOAT g1 = MAX ( fabsl(db_r), fabsl(db_i));
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rtmax = sqrt(safmax / 4.);
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if ( f1 > rtmin && f1 < rtmax && g1 > rtmin && g1 < rtmax) { //unscaled
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long double h = ada + adb;
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double adahsq = sqrt(ada * h);
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if (ada >= h *safmin) {
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*C = sqrt(ada/h);
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*R = *DA / *C;
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*(R+1) = *(DA+1) / *(C+1);
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rtmax *= 2.;
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if ( ada > rtmin && h < rtmax) { // no risk of intermediate overflow
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*S = *S1 * (*DA / adahsq) - *(S1+1)* (*(DA+1)/adahsq);
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*(S+1) = *S1 * (*(DA+1) / adahsq) + *(S1+1) * (*DA/adahsq);
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} else {
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*S = *S1 * (*R/h) - *(S1+1) * (*(R+1)/h);
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*(S+1) = *S1 * (*(R+1)/h) + *(S1+1) * (*(R)/h);
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}
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} else {
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*C = ada / adahsq;
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if (*C >= safmin) {
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*R = *DA / *C;
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*(R+1) = *(DA+1) / *(C+1);
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} else {
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*R = *DA * (h / adahsq);
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*(R+1) = *(DA+1) * (h / adahsq);
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}
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*S = *S1 * ada / adahsq;
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*(S+1) = *(S1+1) * ada / adahsq;
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}
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*DA=*R;
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*(DA+1)=*(R+1);
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return;
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} else { // scaled
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FLOAT fs_r, fs_i, gs_r, gs_i;
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long double v,w,f2,g2,h;
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long double u = MIN ( safmax, MAX ( safmin, MAX(f1,g1)));
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gs_r = db_r/u;
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gs_i = db_i/u;
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g2 = sqrt ( gs_r*gs_r + gs_i*gs_i);
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if (f1 /u < rtmin) {
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v = MIN (safmax, MAX (safmin, f1));
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w = v / u;
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fs_r = *DA/ v;
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fs_i = *(DA+1) / v;
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f2 = sqrt ( fs_r*fs_r + fs_i*fs_i);
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h = f2 * w * w + g2;
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} else { // use same scaling for both
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w = 1.;
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fs_r = *DA/ u;
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fs_i = *(DA+1) / u;
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f2 = sqrt ( fs_r*fs_r + fs_i*fs_i);
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h = f2 + g2;
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}
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if ( f2 >= h * safmin) {
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*C = sqrt ( f2 / h );
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*DA = fs_r / *C;
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*(DA+1) = fs_i / *C;
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rtmax *= 2;
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if ( f2 > rtmin && h < rtmax) {
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*S = gs_r * (fs_r /sqrt(f2*h)) - gs_i * (fs_i / sqrt(f2*h));
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*(S+1) = gs_r * (fs_i /sqrt(f2*h)) + gs_i * -1. * (fs_r / sqrt(f2*h));
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} else {
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*S = gs_r * (*DA/h) - gs_i * (*(DA+1) / h);
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*(S+1) = gs_r * (*(DA+1) /h) + gs_i * -1. * (*DA / h);
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}
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} else { // intermediates might overflow
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d = sqrt ( f2 * h);
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*C = f2 /d;
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if (*C >= safmin) {
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*DA = fs_r / *C;
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*(DA+1) = fs_i / *C;
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} else {
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*DA = fs_r * (h / d);
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*(DA+1) = fs_i / (h / d);
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}
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*S = gs_r * (fs_r /d) - gs_i * (fs_i / d);
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*(S+1) = gs_r * (fs_i /d) + gs_i * -1. * (fs_r / d);
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}
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*C *= w;
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*DA *= u;
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*(DA+1) *= u;
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return;
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}
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}
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}
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